Let’s say you have a new health care treatment. How much is someone willing to pay for it?
One way to find out is with a first price sealed-bid auction. In this type of auction, you ask people how much they pay and if they have the highest bid, they get the item. In this approach, however, the winner will get zero utility/profits since their bid would match their willingness to pay. It has been shown that if valuations are drawn from bidders form a uniform distribution, then the optimal bid is half of willingness to pay.
The Becker–DeGroot–Marschak (BDM) mechanism solves this problem. It asks people to submit a bid, b, for an item. Then a random price, p, is drawn. If the bid is higher than the price (i.e., b>p) then the individual wins the item. However, the price they pay is not their bid but instead the random price p. If their bid is lower than the random price, they do not get the item. [In the case where b=p, once could consider the case where the person would get the item half the time].
Why does this approach lead to an honest willingness to pay answer?
Consider the case if the person submits a bit higher then their real willingness to pay (i.e., b>WTP). If the price is higher than their WTP but below b, then the individual will be paying more than what it is worth. What if the bid is below their WTP (i.e., b<WTP)? In this case, they have no price advantage because the maximum price they would pay is p. If however, p falls between b and WTP, then the individual will not get the item even though their valuation was higher than the price. Thus, it is incentive compatible to bid your willingness to pay.
The BDM mechanism is similar to a Vickrey auction (or second-price sealed bid auction if a single indivisible good is being sold). The Vickrey auction is similar to the BDM mechanism. In the Vickrey auction, however, the winner has the highest but; instead of paying the random price or their bid, the winner pays the bid of the second highest bidder. Similar to the logic above, in this case, individuals have an incentive to bid their true willingness to pay.
While both auctions are able to elicit true WTP, they may not maximize the revenue the seller collects.
Nevertheless, BDM is a helpful mechanism for measuring WTP for research purposes. For instance, Aylward et al. (2020) uses BDM to measure WTP for HIV self-tests.
Self‐tests offer one approach for reducing frictions underlying low demand for preventive health inputs, yet there is little evidence on demand for self‐tests. We used the Becker–DeGroot–Marschak mechanism—an incentive‐compatible approach—to elicit exact willingness to pay (WTP) for HIV self‐tests in a field experiment with 822 participants at 66 health clinics/pharmacies in Kenya. Our analysis reveals substantial demand at low prices and highly elastic demand at a wide range of prices above this range. We find few participants with nonpositive WTP. We examine correlates of WTP and discuss policy and research implications of our findings.